The Padovan sequence and the Narayana sequence represent two classical instances of third-order linear recurrence streams, which are established via the respective structural relations P_n= P_(n-2)+ P_(n-3) with the starting configuration (P_0,P_1,P_2 )= (1,1,1), and N_m= N_(m-1)+ N_(m-3) under the primary values (N_0,N_1,N_2 )= (0,1,1). This paper is dedicated to providing a comprehensive analysis regarding the multiplicative dependency between these two separate recursive structures.